51,661 research outputs found
Towards Efficient Maximum Likelihood Estimation of LPV-SS Models
How to efficiently identify multiple-input multiple-output (MIMO) linear
parameter-varying (LPV) discrete-time state-space (SS) models with affine
dependence on the scheduling variable still remains an open question, as
identification methods proposed in the literature suffer heavily from the curse
of dimensionality and/or depend on over-restrictive approximations of the
measured signal behaviors. However, obtaining an SS model of the targeted
system is crucial for many LPV control synthesis methods, as these synthesis
tools are almost exclusively formulated for the aforementioned representation
of the system dynamics. Therefore, in this paper, we tackle the problem by
combining state-of-the-art LPV input-output (IO) identification methods with an
LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step.
The resulting modular LPV-SS identification approach achieves statical
efficiency with a relatively low computational load. The method contains the
following three steps: 1) estimation of the Markov coefficient sequence of the
underlying system using correlation analysis or Bayesian impulse response
estimation, then 2) LPV-SS realization of the estimated coefficients by using a
basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate
from a maximum-likelihood point of view by a gradient-based or an
expectation-maximization optimization methodology. The effectiveness of the
full identification scheme is demonstrated by a Monte Carlo study where our
proposed method is compared to existing schemes for identifying a MIMO LPV
system
Model-based Recursive Partitioning for Subgroup Analyses
The identification of patient subgroups with differential treatment effects
is the first step towards individualised treatments. A current draft guideline
by the EMA discusses potentials and problems in subgroup analyses and
formulated challenges to the development of appropriate statistical procedures
for the data-driven identification of patient subgroups. We introduce
model-based recursive partitioning as a procedure for the automated detection
of patient subgroups that are identifiable by predictive factors. The method
starts with a model for the overall treatment effect as defined for the primary
analysis in the study protocol and uses measures for detecting parameter
instabilities in this treatment effect. The procedure produces a segmented
model with differential treatment parameters corresponding to each patient
subgroup. The subgroups are linked to predictive factors by means of a decision
tree. The method is applied to the search for subgroups of patients suffering
from amyotrophic lateral sclerosis that differ with respect to their Riluzole
treatment effect, the only currently approved drug for this disease.Comment: 26 pages, 6 figure
Bayesian Regularisation in Structured Additive Regression Models for Survival Data
During recent years, penalized likelihood approaches have attracted a lot of interest both in the area of semiparametric regression and for the regularization of high-dimensional regression models. In this paper, we introduce a Bayesian formulation that allows to combine both aspects into a joint regression model with a focus on hazard regression for survival times. While Bayesian penalized splines form the basis for estimating nonparametric and flexible time-varying effects, regularization of high-dimensional covariate vectors is based on scale mixture of normals priors. This class of priors allows to keep a (conditional) Gaussian prior for regression coefficients on the predictor stage of the model but introduces suitable mixture distributions for the Gaussian variance to achieve regularization. This scale mixture property allows to device general and adaptive Markov chain Monte Carlo simulation algorithms for fitting a variety of hazard regression models. In particular, unifying algorithms based on iteratively weighted least squares proposals can be employed both for regularization and penalized semiparametric function estimation. Since sampling based estimates do no longer have the variable selection property well-known for the Lasso in frequentist analyses, we additionally consider spike and slab priors that introduce a further mixing stage that allows to separate between influential and redundant parameters. We demonstrate the different shrinkage properties with three simulation settings and apply the methods to the PBC Liver dataset
The Effects of Aquatic Invasive Species on Property Values: Evidence from a Quasi-random Experiment
This study uses hedonic analysis to estimate the effects of a common aquatic invasive species--Eurasian Watermilfoil (milfoil)--on property values across an extensive system of over 170 lakes in the northern forest region of Wisconsin. Since milfoil is inadvertently spread by recreational boaters, and since boaters are more likely to visit attractive lakes, variables indicating the presence of milfoil are endogenous in a hedonic model. Using an identification strategy based on a spatial difference-in-differences specification, results indicate that lakes invaded with milfoil experienced an average 13% decrease in land values after invasion.
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The role of hydrograph indices in parameter estimation of rainfall-runoff models
A reliable prediction of hydrologic models, among other things, requires a set of plausible parameters that correspond with physiographic properties of the basin. This study proposes a parameter estimation approach, which is based on extracting, through hydrograph diagnoses, information in the form of indices that carry intrinsic properties of a basin. This concept is demonstrated by introducing two indices that describe the shape of a streamflow hydrograph in an integrated manner. Nineteen mid-size (223-4790 km2) perennial headwater basins with a long record of streamflow data were selected to evaluate the ability of these indices to capture basin response characteristics. An examination of the utility of the proposed indices in parameter estimation is conducted for a five-parameter hydrologic model using data from the Leaf River, located in Fort Collins, Mississippi. It is shown that constraining the parameter estimation by selecting only those parameters that result in model output which maintains the indices as found in the historical data can improve the reliability of model predictions. These improvements were manifested in (a) improvement of the prediction of low and high flow, (b) improvement of the overall total biases, and (c) maintenance of the hydrograph's shape for both long-term and short-term predictions. Copyright © 2005 John Wiley & Sons, Ltd
Structured Learning in Time-dependent Cox Models
Cox models with time-dependent coefficients and covariates are widely used in
survival analysis. In high-dimensional settings, sparse regularization
techniques are employed for variable selection, but existing methods for
time-dependent Cox models lack flexibility in enforcing specific sparsity
patterns (i.e., covariate structures). We propose a flexible framework for
variable selection in time-dependent Cox models, accommodating complex
selection rules. Our method can adapt to arbitrary grouping structures,
including interaction selection, temporal, spatial, tree, and directed acyclic
graph structures. It achieves accurate estimation with low false alarm rates.
We develop the sox package, implementing a network flow algorithm for
efficiently solving models with complex covariate structures. Sox offers a
user-friendly interface for specifying grouping structures and delivers fast
computation. Through examples, including a case study on identifying predictors
of time to all-cause death in atrial fibrillation patients, we demonstrate the
practical application of our method with specific selection rules.Comment: 49 pages (with 19 pages of appendix),9 tables, 3 figure
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